A Cosmological Scenario without Initial Singularity Bouncing - - PowerPoint PPT Presentation
A Cosmological Scenario without Initial Singularity Bouncing Cosmology Taotao Qiu LeCosPA Center, National Taiwan University 2012-03-02 1 Outline Preliminary: Bouncing Scenario As an Alternative of Inflation Perturbations of
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Preliminary: Bouncing Scenario As an
Perturbations of Bouncing Cosmology vs.
Matter Bounce
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Pre-big bang Scenario
Ekpyrotic Scenario
String gas/Hagedorn Scenario
Non-local SFT Scenario
Bouncing Scenario Inflation can solve many Big-Bang-caused puzzles but suffers initial singularity problem
Cambridge University Press, Cambridge, 1973.
Phys.Rev.Lett.72,3305 (1994).
Phys.Rev.D63:123501 (2001).
……
Alternatives of inflation:
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Singularity problem avoided!
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Contraction: Expansion: Bouncing Point: Nearby:
null energy condition violation! Not Necessarily Unphysical!
From Friedmann Equation:
From the naïve picture, we can see:
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Casimir Effect (from Wikipedia)
NEC instability for perfect fluid maybe not if special effects introduced, e.g. nonlocal effects, see Bouncing Galileon Cosmologies.
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phase is very large;
(also provide mechanism for survival of quantum fluctuations, which Seeds for Large Scale Structure. See perturbation theory later on.)
domination avoided if the spatial curva- ture in the contracting phase when the temperature is comparable to today is not larger than the current value.
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If the energy density at the bounce point is given by the Grand Unification scale ( ), then and the wavelength of a perturbation mode is about Unwanted relics can also be avoided because of the low energy scale
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In order to form structures of our universe that can be observed today. Power spectrum: With spectral index: Observationally, nearly scale-invariant power spectrum ( ) is favored by data!
[astro-ph.CO].
Variables for testing perturbations:
Others: bispectrum, trispectrum, gravitational waves, etc.
Why perturbations?
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Perturbed metric in conformal Newtonian gauge: Perturbation Equations for metric:
where
The spectrum: with index:
Inflation:
Assume: solution:
Curvature perturbation:
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Inflationary cosmology bounce cosmology
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Deruelle-Mukhanov matching conditions
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Bounce + Large field inflation Cai, Qiu, Brandenberger, Piao, Zhang, JCAP 0803: 013,2008. Bounce + Small field inflation Cai, Qiu, Xia, Zhang, . Phys.Rev.D79: 021303,2009. Lee-Wick Bounce Cai, Qiu, Brandenberger, Zhang, Phys.Rev.D80: 023511,2009. Holographic Bounce Cai, Xue, Brandenberger, Zhang, JCAP 0906: 037,2009. Non-minimal coupling Bounce Qiu, Yang, JCAP 1011: 012, 2010; Qiu, Class.Quant.Grav.27: 215013, 2010. Radiation Bounce Karouby, Qiu, Brandenberger, Phys.Rev.D84:04350 5,2011. BOUNCE MODELS Others: Bouncing in Modified Gravity New Ekpyrotic model K-Bounce ………… Galileon Bounce Qiu, Evslin, Cai, Li, Zhang, JCAP 1110:036,2011.
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Perturbed Einstein Equations:
Initial condition: Bunch-Davies vacuum
In the matter-dominant era: Near the bounce point:
with where
Solution: Solution:
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Before bounce: After bounce:
Result: (nearly) scale-invariant power spectrum:
Matching condition: (Deruelle-Mukhanov)
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Sketch plot of perturbation:
Power spectrum and index:
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Can solve the singularity problem as well as
Have different evolution mechanisms of
Can give rise to scale-invariant power
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